1 //===-- llvm/ADT/edit_distance.h - Array edit distance function --- C++ -*-===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 ///
9 /// \file
10 /// This file defines a Levenshtein distance function that works for any two
11 /// sequences, with each element of each sequence being analogous to a character
12 /// in a string.
13 ///
14 //===----------------------------------------------------------------------===//
15 
16 #ifndef LLVM_ADT_EDIT_DISTANCE_H
17 #define LLVM_ADT_EDIT_DISTANCE_H
18 
19 #include "llvm/ADT/ArrayRef.h"
20 #include <algorithm>
21 
22 namespace llvm {
23 
24 /// Determine the edit distance between two sequences.
25 ///
26 /// \param FromArray the first sequence to compare.
27 ///
28 /// \param ToArray the second sequence to compare.
29 ///
30 /// \param Map A Functor to apply to each item of the sequences before
31 /// comparison.
32 ///
33 /// \param AllowReplacements whether to allow element replacements (change one
34 /// element into another) as a single operation, rather than as two operations
35 /// (an insertion and a removal).
36 ///
37 /// \param MaxEditDistance If non-zero, the maximum edit distance that this
38 /// routine is allowed to compute. If the edit distance will exceed that
39 /// maximum, returns \c MaxEditDistance+1.
40 ///
41 /// \returns the minimum number of element insertions, removals, or (if
42 /// \p AllowReplacements is \c true) replacements needed to transform one of
43 /// the given sequences into the other. If zero, the sequences are identical.
44 template <typename T, typename Functor>
45 unsigned ComputeMappedEditDistance(ArrayRef<T> FromArray, ArrayRef<T> ToArray,
46                                    Functor Map, bool AllowReplacements = true,
47                                    unsigned MaxEditDistance = 0) {
48   // The algorithm implemented below is the "classic"
49   // dynamic-programming algorithm for computing the Levenshtein
50   // distance, which is described here:
51   //
52   //   http://en.wikipedia.org/wiki/Levenshtein_distance
53   //
54   // Although the algorithm is typically described using an m x n
55   // array, only one row plus one element are used at a time, so this
56   // implementation just keeps one vector for the row.  To update one entry,
57   // only the entries to the left, top, and top-left are needed.  The left
58   // entry is in Row[x-1], the top entry is what's in Row[x] from the last
59   // iteration, and the top-left entry is stored in Previous.
60   typename ArrayRef<T>::size_type m = FromArray.size();
61   typename ArrayRef<T>::size_type n = ToArray.size();
62 
63   if (MaxEditDistance) {
64     // If the difference in size between the 2 arrays is larger than the max
65     // distance allowed, we can bail out as we will always need at least
66     // MaxEditDistance insertions or removals.
67     typename ArrayRef<T>::size_type AbsDiff = m > n ? m - n : n - m;
68     if (AbsDiff > MaxEditDistance)
69       return MaxEditDistance + 1;
70   }
71 
72   SmallVector<unsigned, 64> Row(n + 1);
73   for (unsigned i = 1; i < Row.size(); ++i)
74     Row[i] = i;
75 
76   for (typename ArrayRef<T>::size_type y = 1; y <= m; ++y) {
77     Row[0] = y;
78     unsigned BestThisRow = Row[0];
79 
80     unsigned Previous = y - 1;
81     const auto &CurItem = Map(FromArray[y - 1]);
82     for (typename ArrayRef<T>::size_type x = 1; x <= n; ++x) {
83       int OldRow = Row[x];
84       if (AllowReplacements) {
85         Row[x] = std::min(Previous + (CurItem == Map(ToArray[x - 1]) ? 0u : 1u),
86                           std::min(Row[x - 1], Row[x]) + 1);
87       }
88       else {
89         if (CurItem == Map(ToArray[x - 1]))
90           Row[x] = Previous;
91         else Row[x] = std::min(Row[x-1], Row[x]) + 1;
92       }
93       Previous = OldRow;
94       BestThisRow = std::min(BestThisRow, Row[x]);
95     }
96 
97     if (MaxEditDistance && BestThisRow > MaxEditDistance)
98       return MaxEditDistance + 1;
99   }
100 
101   unsigned Result = Row[n];
102   return Result;
103 }
104 
105 template <typename T>
106 unsigned ComputeEditDistance(ArrayRef<T> FromArray, ArrayRef<T> ToArray,
107                              bool AllowReplacements = true,
108                              unsigned MaxEditDistance = 0) {
109   return ComputeMappedEditDistance(
110       FromArray, ToArray, [](const T &X) -> const T & { return X; },
111       AllowReplacements, MaxEditDistance);
112 }
113 
114 } // End llvm namespace
115 
116 #endif
117